I think that Twitter is a crime against literacy if you let it be and to be honest I think the damage was already done before people started tweeting. There's a type of writing called microfiction, which I used to like doing when I was at uni, but my limit would be 100 to 200 words, limiting yourself like that can make you creative and it can have powerful results. There's some folks out there who challenge themselves by using tweets, yes, it's very short and simple stuff, but I guess it's like writing a Haiku, playing with words. I remember reading in a writing magazine about a challenge where people would have to pick a classic novel and sum up the plot in the best way possible in a tweet and have folks work out which novel it is - there were some clever attempts IIRC.
However, it's not really Twitter's usage there, still, it might be something interesting to try for Twitterers.
But I am just saying, there's room to try and be clever with Twitter, even if people aren't.
Also, I wouldn't blame technology, but education itself and maybe apathy. 'Txt' is really only for text messages, though I think these days the need to do it is thinned out, with touch phones with full keyboards and the size of text messages is not so much a problem anymore. These days I tend to write in full sentences on my phone. When it comes to arguments on the use of language, I tend to side with Stephen Fry, because I think he makes very good points about it. Hence I feel comfortable with letting myself make so many mistakes on the internet - in any formal writing, it's completely different: anything I've published, stuff I've written when I was at Uni, my novel (though a work in progress), any personal projects and my CV/Resume are all grammatically correct.
Coming back round to Twitter, it's very difficult to get your message across and be grammatically correct at the same time. Writers get to be clever because they get to lie and say their errors are down to style whilst the President doesn't get the same privilege.